CISS has been actively studied
and become an interdisciplinary research fields
spanning physics, chemistry, and biology.
The reported spin-polarization
up to \({60}{\%}\)  amounts to the effective magnetic field
of an order of \({100}{}\) 
 [1]},
which is unrealistically strong.
So far, several attempts have been made on the electron motion in a chiral molecule
in the presence of spin-orbit coupling (SOC)
 [2]}, [3]}, [4]}.
The present status of theoretical studies is well summarized in Ref. [5]}.
In order to find an alternative explanation,
we would like to understand the fact
that CISS effect is observed
even in the organic molecules
with weak SOC strength
in a way
that do not rely explicitly
on the strength of the SOC.
Our belief here
is based on
the importance of interplay
between nuclear and electronic motions
which are governed by
the same symmetry restrictions
in chiral materials.
Moreover,
our objective also
lies on a quest for CISS theory
that do not violate
the time reversal symmetry.
This is exactly
what we address in this Letter.
